Solve for $x$ and $y$ using elimination. $\begin{align*}6x+8y &= -3 \\ -6x+5y &= 3\end{align*}$
Explanation: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $13y = 0$ Divide both sides by $13$ and reduce as necessary. $y = 0$ Substitute $0$ for $y$ in the top equation. $6x+8( 0) = -3$ $6x = -3$ $6x = -3$ $x = -\dfrac{1}{2}$ The solution is $\enspace x = -\dfrac{1}{2}, \enspace y = 0$.